Reparametrizations and metric structures in thermodynamic phase space

We investigate the consequences of reparametrizations in geometric description thermodynamics analyzing effects on thermodynamic phase space. It is known that contact and Riemannian structures space are related to equilibrium statistical fluctuations Boltzmann-Gibbs mechanics. The physical motivation for this analysis rests upon possibility having, instead a direct control intensive parameters determining state corresponding reservoirs, set differentiable functions original variables. Likewise, we consider extensive variables accounting not having access find effect can be codified, geometrical terms, its structures. In particular, single out rank-two tensor enters definition metric which geometrically comprises information about such reparametrizations. notice even if these modified by reparametrizations, structure states preserved.